THE CONSTITUTION OF ARITHMETICAL ABILITIES 63 SHORT DIVISION : DEDUCTIVE EXPLANATION
Divide 1825 by 4
Divisor 4
EXPLANATION. — For convenience we write the divisor at the left of 1825 Dividend *^e dividend, and the quotient be-
_______ low it, and begin at the left to di-
456 J vide. 4 is not contained in 1 thou-
Quotient sand any thousand times, therefore
the quotient contains no unit of
any order higher than hundreds.'
Consequently we find how many times 4 is contained in the hundreds of the dividend. 1 thousand and 8 hundreds are 18 hundreds. 4 is contained in 18 hundreds 4 hundred times and 2 hundreds remaining. We write the 4 hundreds in the quotient. The 2 hundreds we consider as united with the 2 tens, making 22 tens. 4 is contained in 22 tens 5 tens limes, and 2 tens remaining. We write the 5 tens in. the quotient, and the remaining 2 tens we consider as united with the 5 units, making 25 units. 4 is contained in 25 units 6 units times and 1 unit remaining. "We write the 6 units in the quotient and indicate the division of the remainder, 1 tinit, by the divisor 4.
Therefore the quotient of 1825 divided by 4 is 456i, or 456 and 1 remainder.
SHOUT DIVISION : INDUCTIVE EXPLANATION Dividing Large Numbers
1. Tom, Dick, Will, and Fred put in 2 cents each, to buy an
eight-cent bag of marbles. There are 128 marbles in it. How many should each boy have, if they divide the marbles equally among the four boys?
4|T28
Think " 12 = three 4s." Write the 8 over the 2 in the tens
column. Think U8~two 4s." Write the 2 over the 8 in the ones
column. 32 is right, because 4X32 = 128.
2. Mary, Nell, and Alice are going to buy a book as a present
for their Sunday-school teacher. The present costs 69 cents. How much should each girl pay, if they divide the cost equally among the three girls?
3|69"
Think "6= . . .3s." Write the 2 over the 6 in the tens column.